Prospero's response is good, although I'd do one thing differently.
I wouldn't necessarily be too brief or formulaic with a cover letter.
It is your introduction to whomever reads it, after all, and also, it is your first chance to "interview," so to speak, and the one interview opportunity over which you have the most control.
So, make sure to personalize it -- both toward whomever it is written, and regarding yourself. Tell them about yourself, let them get to know you a little bit, and hopefully, get a feel for you, through whatever you write. Make them like you, and be interested in meeting you. If it is a good letter, one that piques their interest, they probably won't mind reading it, even if it's longer than the oft-cited one page in length.
Tell them where you live, where you're going to school, get detailed about what you've done, and mention specific stories you're proud of, especially those that the people at your target paper may have seen, or that you think perhaps, your target paper has not done.
Tell what sports you've covered most, and/or what work you'd like to do, but maybe haven't yet. These may be avenues of opportunity that the target paper may be willing and able to give you. Tell them what days/hours you are available, or would be willing to make yourself so. And if you are handy with a video camera, comfortable on Twitter and into Web site design and production or are learning/knowledgeable about multi-media production, or if you are, in any way, a techno-wiz, then, by all means, mention that...up high. This could be a very useful avenue to work.
Read up on the target paper's recent offerings, and mention some significant ones that you noticed, either for the issue involved, or for any writing that particularly impressed you, and mention that.
Tell the editor something you like about what they do, and why, and maybe, something that you noticed but that you think you might have handled differently. It shows thought, and engagement in their paper, and is evidence that you're interested enough to actually be following it, and not just fishing around for a job, any job, like, oh, thousands of other job hunters out there who also send resumes, and do follow-up calls, and write thank you notes...
Copy-edit the letter well, and have someone else proofread it. Do your level best to catch any spelling errors, grammar mistakes or poorly-written sentences.
Oh, and be sure to include your name, phone number/email address somewhere on it, not just on the resume. Make it easy for them to reach you, even if your cover letter happens to get separated from your resume or clips among the pile that constitutes many newspaper sports editors' desk-top "files."